hw10_sol_sp10 - Physics 101 Classical Physics Spring 2010...

Physics 101 Classical Physics Spring 2010
Homework 10 Solutions
DUE IN CLASS ON April 15
1. If the frequency of a wave is 200 Hz, and the wavelength is 2 m, how much time
is required for a single wave to pass by an observer?
(a) 0.005 s , (b) 0.050 s, (c) 200 s, (d) 400 s, (e) 800 s
Since the frequency is the number of wavelengths that pass a given point per unit time, the
time for a single wave to pass an observer is 1 /f = 0 . 005 s.
2. If the frequency of a wave is 200 Hz, and the wavelength is 2 m, what is the
velocity of the wave?
(a) 0.05 m/s, (b) 0.50 m/s, (c) 200 m/s, (d) 400 m/s , (e) 800 m/s
The velocity is given by the product of the frequency and wavelength v = fλ = 400 m/s.
3. If the frequency of a wave is 200 Hz, and the velocity is 10 m/s, what is the
wavelength?
(a) 0.05 m , (b) 0.50 m, (c) 200 m, (d) 400 m, (e) 800 m
Solving the relation used in problem 2 for the wavelength, λ = v/f = 0 . 05 m.
4. A transverse wave travels along a perfectly elastic string parallel to the ground.
Any given point on the string:
(a) doesn’t move
(b) moves up and down
(c) moves up only
(d) moves left and right
(e) depends on how high off the ground the string is.
5. A standing wave:
(a) can be constructed from two similar waves traveling in opposite directions
(b) must be transverse
(c) must be longitudinal
(d) has motionless points that are closer than half a wavelength
(e) has a wave velocity that differs by a factor of two from what it would be for
a traveling wave
For example, the superposition of 2 waves travelling in opposite direction with the same
frequency and amplitude can be written as
A cos( kx - ωt ) + A cos( kx + ωt ) = 2 A cos( kx ) cos( ωt )
Then a given point at x executes simple harmonic motion, which gives a standing wave.